7 Refractive index of gas 1 weight Another useful application of the Michelson

# 7 refractive index of gas 1 weight another useful

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7. Refractive index of gas (1 weight) Another useful application of the Michelson interferometer is the measurement of the index of refraction of a gas by exploiting the relationship between the index of refraction n and pressure P in the gas chamber. Consider an evacuated cylindrical gas cell, positioned on the viewing axis of mirror A, of length l . Suppose the gas with the index of refraction n is admitted into it. The change in the optical path length will be simply 2 l ( n 1) that gives the exact same relationship as in the previous sect ion, for a light of wavelength λ 2 l ( n 1) = , where N is the number of fringes counted. Take the derivative with respect to pressure: (6) It is an experimental fact that for gases the number n 1 is proportional to the density of the gas ρ , as long as the chemical composition of the gas does not change, i.e. n 1 = c ρ for some constant c [4]. Assume the gas obeys the ideal gas law, m PV = RT M where V is the volume, m and M the total and the molar masses, respectively, R is the universal gas constant and T is the absolute temperature. We will rewrite it in the form 1 t Mf dP dn l dP dN 2